OK, I thought about this a bit more, and the answer became somewhat obvious to me. Music around Mahler's time, particulalry Austro-German music, was full of fanfare-like figures and big "declamatory" statements. Well, there are primarily just three intervals - the musical distance between any two notes - that work for bold and brave sounding, declamatory statements. The first and most obvious is the octave jump. In the same context, the second most important interval is the perfect fifth. But the problem with the perfect fifth is that it has very strong harmonic implications - in fact, "gravity" might be a more accurate description. The lower note of the two is the strongest. Hence, there's a sort of gravitational pull towards the lower note. When you play a perfect fourth interval, there still exists a gravitational pull, but it's not quite as strong as it is with the perfect fifth. It's also the upper note that's the stronger one of the two. Now, if you have a piano or a guitar (or any instrument), and you would like to demonstrate these principles to yourself, I suggest that you print this out and take it over to the piano.
Let's fool around in the key of C, because there are no flats or sharps in the key of C Major. OK; now, plunk a C on the piano, and go plunk the G above the C. You've just played a perfect fifth interval. Now go back and forth between the two notes. You should notice that the lower note will sound the stronger of the two. There's a gravitational pull that makes you want to finish with the lower C. Now, plunk the same C; but this time, plunk the F instead of the G (the F above). That's a perfect fourth interval. Again, go back and forth between the two notes. The pull isn't nearly so strong, but your ear will want to finish on the F. It's the upper note, and it's the stronger of the two. OK, let's start this exercise over. But this time, we'll "invert" the perfect fifth interval by playing the G BELOW our starting C. From G to C is four steps on the piano ("From G to shining Seeeeeea"). Hence, the inversion of a perfect fifth interval becomes a perfect fourth. (or more accurately, IS a perfect fourth). Now you're asking me, so what?
Well, a perfect example of this principal exists right at the very beginning of Mahler's 3rd symphony. The opening unison horn fanfare begins with a perfect fourth interval, and it's clearly the upper note that sounds the stronger of the two. Yet, it's not as overtly "gravitational" as it could have been, if Mahler had written a perfect fifth interval instead. Also, think of Else's wedding processional from "Lohengrin". You know, "Here comes the bride".
Wagner starts with a perfect fourth. And just to drive the point home, he places a dotted eighth/sixteenth note rhythm on the upper note (which leads into a half note: two beats duration in length). Then Wagner starts again from the same lower note, but jumps up to the fifth degree this time. However, to reinforce that the fourth degree is actually our tonal center, Wagner then comes down to the the major third degree, which acts as a "leading tone" back to our fourth degree. Try this on your piano (or guitar, or tuba, or clarinet, or gong, or triangle, etc.).
Start "Here Comes The Bride" on C, and go up to the F. Start it again, but go up to the G; then come down to E, which acts as a "leading tone" back to our F. "Else's Processional" starts with a fanfare-like figure, but it's the upper note that's the tonal center. Why? Because Wagner starts it with a perfect fourth interval, which almost automatically establishes the upper note as being the tonal center - even if only temporarily (depending on what transpires later).
Another great example of this principle exists right at the very end of Mahler's 3rd symphony: the two sets of timpani going back and forth on the notes D and A. But instead of going to the A above the D - which would have been a perfect fifth interval - Mahler goes digs down to the A BELOW the D, thus creating a perfect fourth interval between those two notes. Thus, the INVERSION of a perfect fifth interval is the perfect fourth. Thus, Mahler's 3rd symphony - his biggest and grandest "nature" symphony - starts and ends with the perfect fourth interval.
In the paragraph above, remember that I stated that the perfect fourth is often times associated with folk music? Well, it's also a prominent interval in the Czech music of Smetana and Dvorak. Listen to the very start of Dvorak's 6th symphony, which is one his most "folky" sounding ones. It starts with a very leisurely airing of the perfect fourth interval - not once, but twice! Also, the Czech brothers came far closer to flirting with modal harmonies than their Austro-Germans cousins ever bothered to look into. At times, Brahms came close to implying older, less Major/minor driven modalities. But the Czechs were far ahead in this regard.
In his video lecture, "The Little Drummer Boy", Bernstein points out several places where Mahler implies the Phyrigian mode, which is an ancient mode that's usually associated with Spanish music. In the Mahlerian context, those Phyrigian turns have a more Eastern European sound. To Bernstein's mind, it's all very Jewish sounding. In this particular lecture, Bernstein was focusing heavily upon "Des Knaben Wunderhorn". Again, we have our "folk" connection.
Anyway, while I may not have directly answered your question, I should have presented you with some food for thought.
Barry
Topic: Mahler's use of the interval of the fourth. (Read 7870 times)